LoopStrengthReduce.cpp

  for (IVUsers::const_iterator UI = IU.begin(), E = IU.end(); UI != E; ++UI) {
    // Record the uses.
    LSRFixup &LF = getNewFixup();
    LF.UserInst = UI->getUser();
    LF.OperandValToReplace = UI->getOperandValToReplace();
    LF.PostIncLoops = UI->getPostIncLoops();

    LSRUse::KindType Kind = LSRUse::Basic;
    const Type *AccessTy = 0;
    if (isAddressUse(LF.UserInst, LF.OperandValToReplace)) {
      Kind = LSRUse::Address;
      AccessTy = getAccessType(LF.UserInst);
    }

    const SCEV *S = IU.getExpr(*UI);

    // Equality (== and !=) ICmps are special. We can rewrite (i == N) as
    // (N - i == 0), and this allows (N - i) to be the expression that we work
    // with rather than just N or i, so we can consider the register
    // requirements for both N and i at the same time. Limiting this code to
    // equality icmps is not a problem because all interesting loops use
    // equality icmps, thanks to IndVarSimplify.
    if (ICmpInst *CI = dyn_cast<ICmpInst>(LF.UserInst))
      if (CI->isEquality()) {
        // Swap the operands if needed to put the OperandValToReplace on the
        // left, for consistency.
        Value *NV = CI->getOperand(1);
        if (NV == LF.OperandValToReplace) {
          CI->setOperand(1, CI->getOperand(0));
          CI->setOperand(0, NV);
          NV = CI->getOperand(1);
          Changed = true;
        }

        // x == y  -->  x - y == 0
        const SCEV *N = SE.getSCEV(NV);
        if (N->isLoopInvariant(L)) {
          Kind = LSRUse::ICmpZero;
          S = SE.getMinusSCEV(N, S);
        }

        // -1 and the negations of all interesting strides (except the negation
        // of -1) are now also interesting.
        for (size_t i = 0, e = Factors.size(); i != e; ++i)
          if (Factors[i] != -1)
            Factors.insert(-(uint64_t)Factors[i]);
        Factors.insert(-1);
      }

    // Set up the initial formula for this use.
    std::pair<size_t, int64_t> P = getUse(S, Kind, AccessTy);
    LF.LUIdx = P.first;
    LF.Offset = P.second;
    LSRUse &LU = Uses[LF.LUIdx];
    LU.AllFixupsOutsideLoop &= LF.isUseFullyOutsideLoop(L);

    // If this is the first use of this LSRUse, give it a formula.
    if (LU.Formulae.empty()) {
      InsertInitialFormula(S, LU, LF.LUIdx);
      CountRegisters(LU.Formulae.back(), LF.LUIdx);
    }
  }

  DEBUG(print_fixups(dbgs()));
}

/// InsertInitialFormula - Insert a formula for the given expression into
/// the given use, separating out loop-variant portions from loop-invariant
/// and loop-computable portions.
void
LSRInstance::InsertInitialFormula(const SCEV *S, LSRUse &LU, size_t LUIdx) {
  Formula F;
  F.InitialMatch(S, L, SE, DT);
  bool Inserted = InsertFormula(LU, LUIdx, F);
  assert(Inserted && "Initial formula already exists!"); (void)Inserted;
}

/// InsertSupplementalFormula - Insert a simple single-register formula for
/// the given expression into the given use.
void
LSRInstance::InsertSupplementalFormula(const SCEV *S,
                                       LSRUse &LU, size_t LUIdx) {
  Formula F;
  F.BaseRegs.push_back(S);
  F.AM.HasBaseReg = true;
  bool Inserted = InsertFormula(LU, LUIdx, F);
  assert(Inserted && "Supplemental formula already exists!"); (void)Inserted;
}

/// CountRegisters - Note which registers are used by the given formula,
/// updating RegUses.
void LSRInstance::CountRegisters(const Formula &F, size_t LUIdx) {
  if (F.ScaledReg)
    RegUses.CountRegister(F.ScaledReg, LUIdx);
  for (SmallVectorImpl<const SCEV *>::const_iterator I = F.BaseRegs.begin(),
       E = F.BaseRegs.end(); I != E; ++I)
    RegUses.CountRegister(*I, LUIdx);
}

/// InsertFormula - If the given formula has not yet been inserted, add it to
/// the list, and return true. Return false otherwise.
bool LSRInstance::InsertFormula(LSRUse &LU, unsigned LUIdx, const Formula &F) {
  if (!LU.InsertFormula(F))
    return false;

  CountRegisters(F, LUIdx);
  return true;
}

/// CollectLoopInvariantFixupsAndFormulae - Check for other uses of
/// loop-invariant values which we're tracking. These other uses will pin these
/// values in registers, making them less profitable for elimination.
/// TODO: This currently misses non-constant addrec step registers.
/// TODO: Should this give more weight to users inside the loop?
void
LSRInstance::CollectLoopInvariantFixupsAndFormulae() {
  SmallVector<const SCEV *, 8> Worklist(RegUses.begin(), RegUses.end());
  SmallPtrSet<const SCEV *, 8> Inserted;

  while (!Worklist.empty()) {
    const SCEV *S = Worklist.pop_back_val();

    if (const SCEVNAryExpr *N = dyn_cast<SCEVNAryExpr>(S))
      Worklist.append(N->op_begin(), N->op_end());
    else if (const SCEVCastExpr *C = dyn_cast<SCEVCastExpr>(S))
      Worklist.push_back(C->getOperand());
    else if (const SCEVUDivExpr *D = dyn_cast<SCEVUDivExpr>(S)) {
      Worklist.push_back(D->getLHS());
      Worklist.push_back(D->getRHS());
    } else if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(S)) {
      if (!Inserted.insert(U)) continue;
      const Value *V = U->getValue();
      if (const Instruction *Inst = dyn_cast<Instruction>(V)) {
        // Look for instructions defined outside the loop.
        if (L->contains(Inst)) continue;
      } else if (isa<UndefValue>(V))
        // Undef doesn't have a live range, so it doesn't matter.
        continue;
      for (Value::const_use_iterator UI = V->use_begin(), UE = V->use_end();
           UI != UE; ++UI) {
        const Instruction *UserInst = dyn_cast<Instruction>(*UI);
        // Ignore non-instructions.
        if (!UserInst)
          continue;
        // Ignore instructions in other functions (as can happen with
        // Constants).
        if (UserInst->getParent()->getParent() != L->getHeader()->getParent())
          continue;
        // Ignore instructions not dominated by the loop.
        const BasicBlock *UseBB = !isa<PHINode>(UserInst) ?
          UserInst->getParent() :
          cast<PHINode>(UserInst)->getIncomingBlock(
            PHINode::getIncomingValueNumForOperand(UI.getOperandNo()));
        if (!DT.dominates(L->getHeader(), UseBB))
          continue;
        // Ignore uses which are part of other SCEV expressions, to avoid
        // analyzing them multiple times.
        if (SE.isSCEVable(UserInst->getType())) {
          const SCEV *UserS = SE.getSCEV(const_cast<Instruction *>(UserInst));
          // If the user is a no-op, look through to its uses.
          if (!isa<SCEVUnknown>(UserS))
            continue;
          if (UserS == U) {
            Worklist.push_back(
              SE.getUnknown(const_cast<Instruction *>(UserInst)));
            continue;
          }
        }
        // Ignore icmp instructions which are already being analyzed.
        if (const ICmpInst *ICI = dyn_cast<ICmpInst>(UserInst)) {
          unsigned OtherIdx = !UI.getOperandNo();
          Value *OtherOp = const_cast<Value *>(ICI->getOperand(OtherIdx));
          if (SE.getSCEV(OtherOp)->hasComputableLoopEvolution(L))
            continue;
        }

        LSRFixup &LF = getNewFixup();
        LF.UserInst = const_cast<Instruction *>(UserInst);
        LF.OperandValToReplace = UI.getUse();
        std::pair<size_t, int64_t> P = getUse(S, LSRUse::Basic, 0);
        LF.LUIdx = P.first;
        LF.Offset = P.second;
        LSRUse &LU = Uses[LF.LUIdx];
        LU.AllFixupsOutsideLoop &= LF.isUseFullyOutsideLoop(L);
        InsertSupplementalFormula(U, LU, LF.LUIdx);
        CountRegisters(LU.Formulae.back(), Uses.size() - 1);
        break;
      }
    }
  }
}

/// CollectSubexprs - Split S into subexpressions which can be pulled out into
/// separate registers. If C is non-null, multiply each subexpression by C.
static void CollectSubexprs(const SCEV *S, const SCEVConstant *C,
                            SmallVectorImpl<const SCEV *> &Ops,
                            ScalarEvolution &SE) {
  if (const SCEVAddExpr *Add = dyn_cast<SCEVAddExpr>(S)) {
    // Break out add operands.
    for (SCEVAddExpr::op_iterator I = Add->op_begin(), E = Add->op_end();
         I != E; ++I)
      CollectSubexprs(*I, C, Ops, SE);
    return;
  } else if (const SCEVAddRecExpr *AR = dyn_cast<SCEVAddRecExpr>(S)) {
    // Split a non-zero base out of an addrec.
    if (!AR->getStart()->isZero()) {
      CollectSubexprs(SE.getAddRecExpr(SE.getConstant(AR->getType(), 0),
                                       AR->getStepRecurrence(SE),
                                       AR->getLoop()), C, Ops, SE);
      CollectSubexprs(AR->getStart(), C, Ops, SE);
      return;
    }
  } else if (const SCEVMulExpr *Mul = dyn_cast<SCEVMulExpr>(S)) {
    // Break (C * (a + b + c)) into C*a + C*b + C*c.
    if (Mul->getNumOperands() == 2)
      if (const SCEVConstant *Op0 =
            dyn_cast<SCEVConstant>(Mul->getOperand(0))) {
        CollectSubexprs(Mul->getOperand(1),
                        C ? cast<SCEVConstant>(SE.getMulExpr(C, Op0)) : Op0,
                        Ops, SE);
        return;
      }
  }

  // Otherwise use the value itself.
  Ops.push_back(C ? SE.getMulExpr(C, S) : S);
}

/// GenerateReassociations - Split out subexpressions from adds and the bases of
/// addrecs.
void LSRInstance::GenerateReassociations(LSRUse &LU, unsigned LUIdx,
                                         Formula Base,
                                         unsigned Depth) {
  // Arbitrarily cap recursion to protect compile time.
  if (Depth >= 3) return;

  for (size_t i = 0, e = Base.BaseRegs.size(); i != e; ++i) {
    const SCEV *BaseReg = Base.BaseRegs[i];

    SmallVector<const SCEV *, 8> AddOps;
    CollectSubexprs(BaseReg, 0, AddOps, SE);
    if (AddOps.size() == 1) continue;

    for (SmallVectorImpl<const SCEV *>::const_iterator J = AddOps.begin(),
         JE = AddOps.end(); J != JE; ++J) {
      // Don't pull a constant into a register if the constant could be folded
      // into an immediate field.
      if (isAlwaysFoldable(*J, LU.MinOffset, LU.MaxOffset,
                           Base.getNumRegs() > 1,
                           LU.Kind, LU.AccessTy, TLI, SE))
        continue;

      // Collect all operands except *J.
      SmallVector<const SCEV *, 8> InnerAddOps
        (         ((const SmallVector<const SCEV *, 8> &)AddOps).begin(), J);
      InnerAddOps.append
        (next(J), ((const SmallVector<const SCEV *, 8> &)AddOps).end());

      // Don't leave just a constant behind in a register if the constant could
      // be folded into an immediate field.
      if (InnerAddOps.size() == 1 &&
          isAlwaysFoldable(InnerAddOps[0], LU.MinOffset, LU.MaxOffset,
                           Base.getNumRegs() > 1,
                           LU.Kind, LU.AccessTy, TLI, SE))
        continue;

      const SCEV *InnerSum = SE.getAddExpr(InnerAddOps);
      if (InnerSum->isZero())
        continue;
      Formula F = Base;
      F.BaseRegs[i] = InnerSum;
      F.BaseRegs.push_back(*J);
      if (InsertFormula(LU, LUIdx, F))
        // If that formula hadn't been seen before, recurse to find more like
        // it.
        GenerateReassociations(LU, LUIdx, LU.Formulae.back(), Depth+1);
    }
  }
}

/// GenerateCombinations - Generate a formula consisting of all of the
/// loop-dominating registers added into a single register.
void LSRInstance::GenerateCombinations(LSRUse &LU, unsigned LUIdx,
                                       Formula Base) {
  // This method is only interesting on a plurality of registers.
  if (Base.BaseRegs.size() <= 1) return;

  Formula F = Base;
  F.BaseRegs.clear();
  SmallVector<const SCEV *, 4> Ops;
  for (SmallVectorImpl<const SCEV *>::const_iterator
       I = Base.BaseRegs.begin(), E = Base.BaseRegs.end(); I != E; ++I) {
    const SCEV *BaseReg = *I;
    if (BaseReg->properlyDominates(L->getHeader(), &DT) &&
        !BaseReg->hasComputableLoopEvolution(L))
      Ops.push_back(BaseReg);
    else
      F.BaseRegs.push_back(BaseReg);
  }
  if (Ops.size() > 1) {
    const SCEV *Sum = SE.getAddExpr(Ops);
    // TODO: If Sum is zero, it probably means ScalarEvolution missed an
    // opportunity to fold something. For now, just ignore such cases
    // rather than proceed with zero in a register.
    if (!Sum->isZero()) {
      F.BaseRegs.push_back(Sum);
      (void)InsertFormula(LU, LUIdx, F);
    }
  }
}

/// GenerateSymbolicOffsets - Generate reuse formulae using symbolic offsets.
void LSRInstance::GenerateSymbolicOffsets(LSRUse &LU, unsigned LUIdx,
                                          Formula Base) {
  // We can't add a symbolic offset if the address already contains one.
  if (Base.AM.BaseGV) return;

  for (size_t i = 0, e = Base.BaseRegs.size(); i != e; ++i) {
    const SCEV *G = Base.BaseRegs[i];
    GlobalValue *GV = ExtractSymbol(G, SE);
    if (G->isZero() || !GV)
      continue;
    Formula F = Base;
    F.AM.BaseGV = GV;
    if (!isLegalUse(F.AM, LU.MinOffset, LU.MaxOffset,
                    LU.Kind, LU.AccessTy, TLI))
      continue;
    F.BaseRegs[i] = G;
    (void)InsertFormula(LU, LUIdx, F);
  }
}

/// GenerateConstantOffsets - Generate reuse formulae using symbolic offsets.
void LSRInstance::GenerateConstantOffsets(LSRUse &LU, unsigned LUIdx,
                                          Formula Base) {
  // TODO: For now, just add the min and max offset, because it usually isn't
  // worthwhile looking at everything inbetween.
  SmallVector<int64_t, 4> Worklist;
  Worklist.push_back(LU.MinOffset);
  if (LU.MaxOffset != LU.MinOffset)
    Worklist.push_back(LU.MaxOffset);

  for (size_t i = 0, e = Base.BaseRegs.size(); i != e; ++i) {
    const SCEV *G = Base.BaseRegs[i];

    for (SmallVectorImpl<int64_t>::const_iterator I = Worklist.begin(),
         E = Worklist.end(); I != E; ++I) {
      Formula F = Base;
      F.AM.BaseOffs = (uint64_t)Base.AM.BaseOffs - *I;
      if (isLegalUse(F.AM, LU.MinOffset - *I, LU.MaxOffset - *I,
                     LU.Kind, LU.AccessTy, TLI)) {
        F.BaseRegs[i] = SE.getAddExpr(G, SE.getConstant(G->getType(), *I));

        (void)InsertFormula(LU, LUIdx, F);
      }
    }

    int64_t Imm = ExtractImmediate(G, SE);
    if (G->isZero() || Imm == 0)
      continue;
    Formula F = Base;
    F.AM.BaseOffs = (uint64_t)F.AM.BaseOffs + Imm;
    if (!isLegalUse(F.AM, LU.MinOffset, LU.MaxOffset,
                    LU.Kind, LU.AccessTy, TLI))
      continue;
    F.BaseRegs[i] = G;
    (void)InsertFormula(LU, LUIdx, F);
  }
}

/// GenerateICmpZeroScales - For ICmpZero, check to see if we can scale up
/// the comparison. For example, x == y -> x*c == y*c.
void LSRInstance::GenerateICmpZeroScales(LSRUse &LU, unsigned LUIdx,
                                         Formula Base) {
  if (LU.Kind != LSRUse::ICmpZero) return;

  // Determine the integer type for the base formula.
  const Type *IntTy = Base.getType();
  if (!IntTy) return;
  if (SE.getTypeSizeInBits(IntTy) > 64) return;

  // Don't do this if there is more than one offset.
  if (LU.MinOffset != LU.MaxOffset) return;

  assert(!Base.AM.BaseGV && "ICmpZero use is not legal!");

  // Check each interesting stride.
  for (SmallSetVector<int64_t, 8>::const_iterator
       I = Factors.begin(), E = Factors.end(); I != E; ++I) {
    int64_t Factor = *I;
    Formula F = Base;

    // Check that the multiplication doesn't overflow.
    if (F.AM.BaseOffs == INT64_MIN && Factor == -1)
      continue;
    F.AM.BaseOffs = (uint64_t)Base.AM.BaseOffs * Factor;
    if (F.AM.BaseOffs / Factor != Base.AM.BaseOffs)
      continue;

    // Check that multiplying with the use offset doesn't overflow.
    int64_t Offset = LU.MinOffset;
    if (Offset == INT64_MIN && Factor == -1)
      continue;
    Offset = (uint64_t)Offset * Factor;
    if (Offset / Factor != LU.MinOffset)
      continue;

    // Check that this scale is legal.
    if (!isLegalUse(F.AM, Offset, Offset, LU.Kind, LU.AccessTy, TLI))
      continue;

    // Compensate for the use having MinOffset built into it.
    F.AM.BaseOffs = (uint64_t)F.AM.BaseOffs + Offset - LU.MinOffset;

    const SCEV *FactorS = SE.getConstant(IntTy, Factor);

    // Check that multiplying with each base register doesn't overflow.
    for (size_t i = 0, e = F.BaseRegs.size(); i != e; ++i) {
      F.BaseRegs[i] = SE.getMulExpr(F.BaseRegs[i], FactorS);
      if (getExactSDiv(F.BaseRegs[i], FactorS, SE) != Base.BaseRegs[i])
        goto next;
    }

    // Check that multiplying with the scaled register doesn't overflow.
    if (F.ScaledReg) {
      F.ScaledReg = SE.getMulExpr(F.ScaledReg, FactorS);
      if (getExactSDiv(F.ScaledReg, FactorS, SE) != Base.ScaledReg)
        continue;
    }

    // If we make it here and it's legal, add it.
    (void)InsertFormula(LU, LUIdx, F);
  next:;
  }
}

/// GenerateScales - Generate stride factor reuse formulae by making use of
/// scaled-offset address modes, for example.
void LSRInstance::GenerateScales(LSRUse &LU, unsigned LUIdx, Formula Base) {
  // Determine the integer type for the base formula.
  const Type *IntTy = Base.getType();
  if (!IntTy) return;

  // If this Formula already has a scaled register, we can't add another one.
  if (Base.AM.Scale != 0) return;

  // Check each interesting stride.
  for (SmallSetVector<int64_t, 8>::const_iterator
       I = Factors.begin(), E = Factors.end(); I != E; ++I) {
    int64_t Factor = *I;

    Base.AM.Scale = Factor;
    Base.AM.HasBaseReg = Base.BaseRegs.size() > 1;
    // Check whether this scale is going to be legal.
    if (!isLegalUse(Base.AM, LU.MinOffset, LU.MaxOffset,
                    LU.Kind, LU.AccessTy, TLI)) {
      // As a special-case, handle special out-of-loop Basic users specially.
      // TODO: Reconsider this special case.
      if (LU.Kind == LSRUse::Basic &&
          isLegalUse(Base.AM, LU.MinOffset, LU.MaxOffset,
                     LSRUse::Special, LU.AccessTy, TLI) &&
          LU.AllFixupsOutsideLoop)
        LU.Kind = LSRUse::Special;
      else
        continue;
    }
    // For an ICmpZero, negating a solitary base register won't lead to
    // new solutions.
    if (LU.Kind == LSRUse::ICmpZero &&
        !Base.AM.HasBaseReg && Base.AM.BaseOffs == 0 && !Base.AM.BaseGV)
      continue;
    // For each addrec base reg, apply the scale, if possible.
    for (size_t i = 0, e = Base.BaseRegs.size(); i != e; ++i)
      if (const SCEVAddRecExpr *AR =
            dyn_cast<SCEVAddRecExpr>(Base.BaseRegs[i])) {
        const SCEV *FactorS = SE.getConstant(IntTy, Factor);
        if (FactorS->isZero())
          continue;
        // Divide out the factor, ignoring high bits, since we'll be
        // scaling the value back up in the end.
        if (const SCEV *Quotient = getExactSDiv(AR, FactorS, SE, true)) {
          // TODO: This could be optimized to avoid all the copying.
          Formula F = Base;
          F.ScaledReg = Quotient;
          F.DeleteBaseReg(F.BaseRegs[i]);
          (void)InsertFormula(LU, LUIdx, F);
        }
      }
  }
}

/// GenerateTruncates - Generate reuse formulae from different IV types.
void LSRInstance::GenerateTruncates(LSRUse &LU, unsigned LUIdx, Formula Base) {
  // This requires TargetLowering to tell us which truncates are free.
  if (!TLI) return;

  // Don't bother truncating symbolic values.
  if (Base.AM.BaseGV) return;

  // Determine the integer type for the base formula.
  const Type *DstTy = Base.getType();
  if (!DstTy) return;
  DstTy = SE.getEffectiveSCEVType(DstTy);

  for (SmallSetVector<const Type *, 4>::const_iterator
       I = Types.begin(), E = Types.end(); I != E; ++I) {
    const Type *SrcTy = *I;
    if (SrcTy != DstTy && TLI->isTruncateFree(SrcTy, DstTy)) {
      Formula F = Base;

      if (F.ScaledReg) F.ScaledReg = SE.getAnyExtendExpr(F.ScaledReg, *I);
      for (SmallVectorImpl<const SCEV *>::iterator J = F.BaseRegs.begin(),
           JE = F.BaseRegs.end(); J != JE; ++J)
        *J = SE.getAnyExtendExpr(*J, SrcTy);

      // TODO: This assumes we've done basic processing on all uses and
      // have an idea what the register usage is.
      if (!F.hasRegsUsedByUsesOtherThan(LUIdx, RegUses))
        continue;

      (void)InsertFormula(LU, LUIdx, F);
    }
  }
}

namespace {

/// WorkItem - Helper class for GenerateCrossUseConstantOffsets. It's used to
/// defer modifications so that the search phase doesn't have to worry about
/// the data structures moving underneath it.
struct WorkItem {
  size_t LUIdx;
  int64_t Imm;
  const SCEV *OrigReg;

  WorkItem(size_t LI, int64_t I, const SCEV *R)
    : LUIdx(LI), Imm(I), OrigReg(R) {}

  void print(raw_ostream &OS) const;
  void dump() const;
};

}

void WorkItem::print(raw_ostream &OS) const {
  OS << "in formulae referencing " << *OrigReg << " in use " << LUIdx
     << " , add offset " << Imm;
}

void WorkItem::dump() const {
  print(errs()); errs() << '\n';
}

/// GenerateCrossUseConstantOffsets - Look for registers which are a constant
/// distance apart and try to form reuse opportunities between them.
void LSRInstance::GenerateCrossUseConstantOffsets() {
  // Group the registers by their value without any added constant offset.
  typedef std::map<int64_t, const SCEV *> ImmMapTy;
  typedef DenseMap<const SCEV *, ImmMapTy> RegMapTy;
  RegMapTy Map;
  DenseMap<const SCEV *, SmallBitVector> UsedByIndicesMap;
  SmallVector<const SCEV *, 8> Sequence;
  for (RegUseTracker::const_iterator I = RegUses.begin(), E = RegUses.end();
       I != E; ++I) {
    const SCEV *Reg = *I;
    int64_t Imm = ExtractImmediate(Reg, SE);
    std::pair<RegMapTy::iterator, bool> Pair =
      Map.insert(std::make_pair(Reg, ImmMapTy()));
    if (Pair.second)
      Sequence.push_back(Reg);
    Pair.first->second.insert(std::make_pair(Imm, *I));
    UsedByIndicesMap[Reg] |= RegUses.getUsedByIndices(*I);
  }

  // Now examine each set of registers with the same base value. Build up
  // a list of work to do and do the work in a separate step so that we're
  // not adding formulae and register counts while we're searching.
  SmallVector<WorkItem, 32> WorkItems;
  SmallSet<std::pair<size_t, int64_t>, 32> UniqueItems;
  for (SmallVectorImpl<const SCEV *>::const_iterator I = Sequence.begin(),
       E = Sequence.end(); I != E; ++I) {
    const SCEV *Reg = *I;
    const ImmMapTy &Imms = Map.find(Reg)->second;

    // It's not worthwhile looking for reuse if there's only one offset.
    if (Imms.size() == 1)
      continue;

    DEBUG(dbgs() << "Generating cross-use offsets for " << *Reg << ':';
          for (ImmMapTy::const_iterator J = Imms.begin(), JE = Imms.end();
               J != JE; ++J)
            dbgs() << ' ' << J->first;
          dbgs() << '\n');

    // Examine each offset.
    for (ImmMapTy::const_iterator J = Imms.begin(), JE = Imms.end();
         J != JE; ++J) {
      const SCEV *OrigReg = J->second;

      int64_t JImm = J->first;
      const SmallBitVector &UsedByIndices = RegUses.getUsedByIndices(OrigReg);

      if (!isa<SCEVConstant>(OrigReg) &&
          UsedByIndicesMap[Reg].count() == 1) {
        DEBUG(dbgs() << "Skipping cross-use reuse for " << *OrigReg << '\n');
        continue;
      }

      // Conservatively examine offsets between this orig reg a few selected
      // other orig regs.
      ImmMapTy::const_iterator OtherImms[] = {
        Imms.begin(), prior(Imms.end()),
        Imms.upper_bound((Imms.begin()->first + prior(Imms.end())->first) / 2)
      };
      for (size_t i = 0, e = array_lengthof(OtherImms); i != e; ++i) {
        ImmMapTy::const_iterator M = OtherImms[i];
        if (M == J || M == JE) continue;

        // Compute the difference between the two.
        int64_t Imm = (uint64_t)JImm - M->first;
        for (int LUIdx = UsedByIndices.find_first(); LUIdx != -1;
             LUIdx = UsedByIndices.find_next(LUIdx))
          // Make a memo of this use, offset, and register tuple.
          if (UniqueItems.insert(std::make_pair(LUIdx, Imm)))
            WorkItems.push_back(WorkItem(LUIdx, Imm, OrigReg));
      }
    }
  }

  Map.clear();
  Sequence.clear();
  UsedByIndicesMap.clear();
  UniqueItems.clear();

  // Now iterate through the worklist and add new formulae.
  for (SmallVectorImpl<WorkItem>::const_iterator I = WorkItems.begin(),
       E = WorkItems.end(); I != E; ++I) {
    const WorkItem &WI = *I;
    size_t LUIdx = WI.LUIdx;
    LSRUse &LU = Uses[LUIdx];
    int64_t Imm = WI.Imm;
    const SCEV *OrigReg = WI.OrigReg;

    const Type *IntTy = SE.getEffectiveSCEVType(OrigReg->getType());
    const SCEV *NegImmS = SE.getSCEV(ConstantInt::get(IntTy, -(uint64_t)Imm));
    unsigned BitWidth = SE.getTypeSizeInBits(IntTy);

    // TODO: Use a more targeted data structure.
    for (size_t L = 0, LE = LU.Formulae.size(); L != LE; ++L) {
      const Formula &F = LU.Formulae[L];
      // Use the immediate in the scaled register.
      if (F.ScaledReg == OrigReg) {
        int64_t Offs = (uint64_t)F.AM.BaseOffs +
                       Imm * (uint64_t)F.AM.Scale;
        // Don't create 50 + reg(-50).
        if (F.referencesReg(SE.getSCEV(
                   ConstantInt::get(IntTy, -(uint64_t)Offs))))
          continue;
        Formula NewF = F;
        NewF.AM.BaseOffs = Offs;
        if (!isLegalUse(NewF.AM, LU.MinOffset, LU.MaxOffset,
                        LU.Kind, LU.AccessTy, TLI))
          continue;
        NewF.ScaledReg = SE.getAddExpr(NegImmS, NewF.ScaledReg);

        // If the new scale is a constant in a register, and adding the constant
        // value to the immediate would produce a value closer to zero than the
        // immediate itself, then the formula isn't worthwhile.
        if (const SCEVConstant *C = dyn_cast<SCEVConstant>(NewF.ScaledReg))
          if (C->getValue()->getValue().isNegative() !=
                (NewF.AM.BaseOffs < 0) &&
              (C->getValue()->getValue().abs() * APInt(BitWidth, F.AM.Scale))
                .ule(abs64(NewF.AM.BaseOffs)))
            continue;

        // OK, looks good.
        (void)InsertFormula(LU, LUIdx, NewF);
      } else {
        // Use the immediate in a base register.
        for (size_t N = 0, NE = F.BaseRegs.size(); N != NE; ++N) {
          const SCEV *BaseReg = F.BaseRegs[N];
          if (BaseReg != OrigReg)
            continue;
          Formula NewF = F;
          NewF.AM.BaseOffs = (uint64_t)NewF.AM.BaseOffs + Imm;
          if (!isLegalUse(NewF.AM, LU.MinOffset, LU.MaxOffset,
                          LU.Kind, LU.AccessTy, TLI))
            continue;
          NewF.BaseRegs[N] = SE.getAddExpr(NegImmS, BaseReg);

          // If the new formula has a constant in a register, and adding the
          // constant value to the immediate would produce a value closer to
          // zero than the immediate itself, then the formula isn't worthwhile.
          for (SmallVectorImpl<const SCEV *>::const_iterator
               J = NewF.BaseRegs.begin(), JE = NewF.BaseRegs.end();
               J != JE; ++J)
            if (const SCEVConstant *C = dyn_cast<SCEVConstant>(*J))
              if ((C->getValue()->getValue() + NewF.AM.BaseOffs).abs().slt(
                   abs64(NewF.AM.BaseOffs)) &&
                  (C->getValue()->getValue() +
                   NewF.AM.BaseOffs).countTrailingZeros() >=
                   CountTrailingZeros_64(NewF.AM.BaseOffs))
                goto skip_formula;

          // Ok, looks good.
          (void)InsertFormula(LU, LUIdx, NewF);
          break;
        skip_formula:;
        }
      }
    }
  }
}

/// GenerateAllReuseFormulae - Generate formulae for each use.
void
LSRInstance::GenerateAllReuseFormulae() {
  // This is split into multiple loops so that hasRegsUsedByUsesOtherThan
  // queries are more precise.
  for (size_t LUIdx = 0, NumUses = Uses.size(); LUIdx != NumUses; ++LUIdx) {
    LSRUse &LU = Uses[LUIdx];
    for (size_t i = 0, f = LU.Formulae.size(); i != f; ++i)
      GenerateReassociations(LU, LUIdx, LU.Formulae[i]);
    for (size_t i = 0, f = LU.Formulae.size(); i != f; ++i)
      GenerateCombinations(LU, LUIdx, LU.Formulae[i]);
  }
  for (size_t LUIdx = 0, NumUses = Uses.size(); LUIdx != NumUses; ++LUIdx) {
    LSRUse &LU = Uses[LUIdx];
    for (size_t i = 0, f = LU.Formulae.size(); i != f; ++i)
      GenerateSymbolicOffsets(LU, LUIdx, LU.Formulae[i]);
    for (size_t i = 0, f = LU.Formulae.size(); i != f; ++i)
      GenerateConstantOffsets(LU, LUIdx, LU.Formulae[i]);
    for (size_t i = 0, f = LU.Formulae.size(); i != f; ++i)
      GenerateICmpZeroScales(LU, LUIdx, LU.Formulae[i]);
    for (size_t i = 0, f = LU.Formulae.size(); i != f; ++i)
      GenerateScales(LU, LUIdx, LU.Formulae[i]);
  }
  for (size_t LUIdx = 0, NumUses = Uses.size(); LUIdx != NumUses; ++LUIdx) {
    LSRUse &LU = Uses[LUIdx];
    for (size_t i = 0, f = LU.Formulae.size(); i != f; ++i)
      GenerateTruncates(LU, LUIdx, LU.Formulae[i]);
  }

  GenerateCrossUseConstantOffsets();
}

/// If their are multiple formulae with the same set of registers used
/// by other uses, pick the best one and delete the others.
void LSRInstance::FilterOutUndesirableDedicatedRegisters() {
#ifndef NDEBUG
  bool ChangedFormulae = false;
#endif

  // Collect the best formula for each unique set of shared registers. This
  // is reset for each use.
  typedef DenseMap<SmallVector<const SCEV *, 2>, size_t, UniquifierDenseMapInfo>
    BestFormulaeTy;
  BestFormulaeTy BestFormulae;

  for (size_t LUIdx = 0, NumUses = Uses.size(); LUIdx != NumUses; ++LUIdx) {
    LSRUse &LU = Uses[LUIdx];
    FormulaSorter Sorter(L, LU, SE, DT);
    DEBUG(dbgs() << "Filtering for use "; LU.print(dbgs()); dbgs() << '\n');

    bool Any = false;
    for (size_t FIdx = 0, NumForms = LU.Formulae.size();
         FIdx != NumForms; ++FIdx) {
      Formula &F = LU.Formulae[FIdx];

      SmallVector<const SCEV *, 2> Key;
      for (SmallVectorImpl<const SCEV *>::const_iterator J = F.BaseRegs.begin(),
           JE = F.BaseRegs.end(); J != JE; ++J) {
        const SCEV *Reg = *J;
        if (RegUses.isRegUsedByUsesOtherThan(Reg, LUIdx))
          Key.push_back(Reg);
      }
      if (F.ScaledReg &&
          RegUses.isRegUsedByUsesOtherThan(F.ScaledReg, LUIdx))
        Key.push_back(F.ScaledReg);
      // Unstable sort by host order ok, because this is only used for
      // uniquifying.
      std::sort(Key.begin(), Key.end());

      std::pair<BestFormulaeTy::const_iterator, bool> P =
        BestFormulae.insert(std::make_pair(Key, FIdx));
      if (!P.second) {
        Formula &Best = LU.Formulae[P.first->second];
        if (Sorter.operator()(F, Best))
          std::swap(F, Best);
        DEBUG(dbgs() << "  Filtering out formula "; F.print(dbgs());
              dbgs() << "\n"
                        "    in favor of formula "; Best.print(dbgs());
              dbgs() << '\n');
#ifndef NDEBUG
        ChangedFormulae = true;
#endif
        LU.DeleteFormula(F);
        --FIdx;
        --NumForms;
        Any = true;
        continue;
      }
    }

    // Now that we've filtered out some formulae, recompute the Regs set.
    if (Any)
      LU.RecomputeRegs(LUIdx, RegUses);

    // Reset this to prepare for the next use.
    BestFormulae.clear();
  }

  DEBUG(if (ChangedFormulae) {
          dbgs() << "\n"
                    "After filtering out undesirable candidates:\n";
          print_uses(dbgs());
        });
}

// This is a rough guess that seems to work fairly well.
static const size_t ComplexityLimit = UINT16_MAX;

/// EstimateSearchSpaceComplexity - Estimate the worst-case number of
/// solutions the solver might have to consider. It almost never considers
/// this many solutions because it prune the search space, but the pruning
/// isn't always sufficient.
size_t LSRInstance::EstimateSearchSpaceComplexity() const {
  uint32_t Power = 1;
  for (SmallVectorImpl<LSRUse>::const_iterator I = Uses.begin(),
       E = Uses.end(); I != E; ++I) {
    size_t FSize = I->Formulae.size();
    if (FSize >= ComplexityLimit) {
      Power = ComplexityLimit;
      break;
    }
    Power *= FSize;
    if (Power >= ComplexityLimit)
      break;
  }
  return Power;
}

/// NarrowSearchSpaceUsingHeuristics - If there are an extraordinary number of
/// formulae to choose from, use some rough heuristics to prune down the number
/// of formulae. This keeps the main solver from taking an extraordinary amount
/// of time in some worst-case scenarios.
void LSRInstance::NarrowSearchSpaceUsingHeuristics() {
  if (EstimateSearchSpaceComplexity() >= ComplexityLimit) {
    DEBUG(dbgs() << "The search space is too complex.\n");

    DEBUG(dbgs() << "Narrowing the search space by eliminating formulae "
                    "which use a superset of registers used by other "
                    "formulae.\n");

    for (size_t LUIdx = 0, NumUses = Uses.size(); LUIdx != NumUses; ++LUIdx) {
      LSRUse &LU = Uses[LUIdx];
      bool Any = false;
      for (size_t i = 0, e = LU.Formulae.size(); i != e; ++i) {
        Formula &F = LU.Formulae[i];
        // Look for a formula with a constant or GV in a register. If the use
        // also has a formula with that same value in an immediate field,
        // delete the one that uses a register.
        for (SmallVectorImpl<const SCEV *>::const_iterator
             I = F.BaseRegs.begin(), E = F.BaseRegs.end(); I != E; ++I) {
          if (const SCEVConstant *C = dyn_cast<SCEVConstant>(*I)) {
            Formula NewF = F;
            NewF.AM.BaseOffs += C->getValue()->getSExtValue();
            NewF.BaseRegs.erase(NewF.BaseRegs.begin() +
                                (I - F.BaseRegs.begin()));
            if (LU.HasFormulaWithSameRegs(NewF)) {
              DEBUG(dbgs() << "  Deleting "; F.print(dbgs()); dbgs() << '\n');
              LU.DeleteFormula(F);
              --i;
              --e;
              Any = true;
              break;
            }
          } else if (const SCEVUnknown *U = dyn_cast<SCEVUnknown>(*I)) {
            if (GlobalValue *GV = dyn_cast<GlobalValue>(U->getValue()))
              if (!F.AM.BaseGV) {
                Formula NewF = F;
                NewF.AM.BaseGV = GV;
                NewF.BaseRegs.erase(NewF.BaseRegs.begin() +
                                    (I - F.BaseRegs.begin()));
                if (LU.HasFormulaWithSameRegs(NewF)) {
                  DEBUG(dbgs() << "  Deleting "; F.print(dbgs());
                        dbgs() << '\n');
                  LU.DeleteFormula(F);
                  --i;
                  --e;
                  Any = true;
                  break;
                }
              }
          }
        }
      }
      if (Any)
        LU.RecomputeRegs(LUIdx, RegUses);
    }

    DEBUG(dbgs() << "After pre-selection:\n";
          print_uses(dbgs()));
  }

  if (EstimateSearchSpaceComplexity() >= ComplexityLimit) {
    DEBUG(dbgs() << "The search space is too complex.\n");

    DEBUG(dbgs() << "Narrowing the search space by assuming that uses "
                    "separated by a constant offset will use the same "
                    "registers.\n");

    // This is especially useful for unrolled loops.

    for (size_t LUIdx = 0, NumUses = Uses.size(); LUIdx != NumUses; ++LUIdx) {
      LSRUse &LU = Uses[LUIdx];
      for (SmallVectorImpl<Formula>::const_iterator I = LU.Formulae.begin(),
           E = LU.Formulae.end(); I != E; ++I) {
        const Formula &F = *I;
        if (F.AM.BaseOffs != 0 && F.AM.Scale == 0) {
          if (LSRUse *LUThatHas = FindUseWithSimilarFormula(F, LU)) {
            if (reconcileNewOffset(*LUThatHas, F.AM.BaseOffs,
                                   /*HasBaseReg=*/false,
                                   LU.Kind, LU.AccessTy)) {
              DEBUG(dbgs() << "  Deleting use "; LU.print(dbgs());
                    dbgs() << '\n');

              LUThatHas->AllFixupsOutsideLoop &= LU.AllFixupsOutsideLoop;

              // Delete formulae from the new use which are no longer legal.
              bool Any = false;
              for (size_t i = 0, e = LUThatHas->Formulae.size(); i != e; ++i) {
                Formula &F = LUThatHas->Formulae[i];
                if (!isLegalUse(F.AM,
                                LUThatHas->MinOffset, LUThatHas->MaxOffset,
                                LUThatHas->Kind, LUThatHas->AccessTy, TLI)) {
                  DEBUG(dbgs() << "  Deleting "; F.print(dbgs());
                        dbgs() << '\n');
                  LUThatHas->DeleteFormula(F);
                  --i;
                  --e;
                  Any = true;
                }
              }
              if (Any)
                LUThatHas->RecomputeRegs(LUThatHas - &Uses.front(), RegUses);

              // Update the relocs to reference the new use.
              for (SmallVectorImpl<LSRFixup>::iterator I = Fixups.begin(),
                   E = Fixups.end(); I != E; ++I) {
                LSRFixup &Fixup = *I;
                if (Fixup.LUIdx == LUIdx) {
                  Fixup.LUIdx = LUThatHas - &Uses.front();
                  Fixup.Offset += F.AM.BaseOffs;
                  DEBUG(errs() << "New fixup has offset "
                               << Fixup.Offset << '\n');
                }
                if (Fixup.LUIdx == NumUses-1)
                  Fixup.LUIdx = LUIdx;
              }

              // Delete the old use.
              DeleteUse(LU);
              --LUIdx;
              --NumUses;
              break;
            }
          }
        }
      }
    }

    DEBUG(dbgs() << "After pre-selection:\n";
          print_uses(dbgs()));
  }

  // With all other options exhausted, loop until the system is simple
  // enough to handle.
  SmallPtrSet<const SCEV *, 4> Taken;
  while (EstimateSearchSpaceComplexity() >= ComplexityLimit) {
    // Ok, we have too many of formulae on our hands to conveniently handle.
    // Use a rough heuristic to thin out the list.
    DEBUG(dbgs() << "The search space is too complex.\n");

    // Pick the register which is used by the most LSRUses, which is likely
    // to be a good reuse register candidate.
    const SCEV *Best = 0;
    unsigned BestNum = 0;
    for (RegUseTracker::const_iterator I = RegUses.begin(), E = RegUses.end();
         I != E; ++I) {
      const SCEV *Reg = *I;
      if (Taken.count(Reg))
        continue;
      if (!Best)
        Best = Reg;
      else {
        unsigned Count = RegUses.getUsedByIndices(Reg).count();
        if (Count > BestNum) {
          Best = Reg;
          BestNum = Count;